Ocean Waves (continued)
their right in the Northern Hemisphere and with the coast on
their left in the Southern Hemisphere.
Like Rossby waves, continental-shelf waves also exist when
the water is stratified. Then they are known as coastally trapped
waves. These propagate along the coast in the same direction as
shelf waves. Continental-shelf and coastally trapped waves play
an important role in the dynamics of sea level and current fluc-
tuations on the continental shelf. Much of the wind-forced ocean
energy on the continental shelf is associated with these waves.
Coastal Kelvin waves
Coastal Kelvin waves, first discussed by Lord Kelvin, are low-
frequency waves quite distinct from Rossby waves. For Kelvin
waves, gravity is the essential restoring force; coastal Kelvin
waves are long gravity waves trapped to a coastal wall by the
Coriolis force. The amplitude of the wave decays exponentially
from the coast. The water velocity perpendicular to the coast
is zero everywhere. Like continental-shelf waves, coastal Kelvin
waves propagate with the coast on their right in the Northern
Hemisphere and on their left in the Southern Hemisphere. The
flow underneath a wave crest is in the direction of wave propa-
gation, so the only way that the Coriolis force can balance the
pressure-gradient force tending to flatten the sea surface is if
the wave propagates with the coast on its right. Similar argu-
ments show that propagation is with the coast on the left in the
Southern Hemisphere.
Since a Kelvin wave is a long-period gravity wave, it can exist
as either an external or internal gravity wave. In the external
case, the wave behaves as though the water is of constant
density and the phase speed (c) is given by the expression gh,
where g is the acceleration due to gravity and h is water depth.
In the internal case, the phase speed also depends on the
rate of density variation with depth. In general, internal Kelvin
waves travel much more slowly than surface Kelvin waves.
Winds and tidal forces effectively generate oceanic coastal
Kelvin waves. Strictly speaking, coastal Kelvin waves exist only
when water of constant depth is bounded by a vertical wall and
such topography in reality never occurs. However, for cases in
which the decay scale is much greater than the distance across
the shelf and slope to the constant-depth deep sea, the wave is
dynamically coastal Kelvin. Such a condition is most often satis-
fied in the external Kelvin case.
Equatorial Kelvin waves
Equatorial Kelvin waves are long gravity waves with phase
speed trapped to the Equator by the Coriolis force. The north-
south amplitude variation is symmetric about the Equator and
bell-shaped. The wave's north-south velocity is zero and the
wave must propagate eastward. Equatorial Kelvin waves exist
at very low frequencies and the internal ones appear to play a
fundamental role in the dynamics of climate fluctuations like
those associated with El Niño.
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